S. Snape suspected snake speech?

[Amy Z]

No: HPFGUIDX 16723

(I searched and didn't find this discussed...if someone remembers it, 
please direct me to the thread if you can.)

The duelling club scene makes me wonder whether Snape already 
suspected that Harry was a Parselmouth and deliberately made him 
confront a snake.

Herewith the scene with much snipping:

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  "Longbottom and Finch-Fletchley, how about you?' [says Lockhart]
  "A bad idea, Professor Lockhart," said Snape . . . . "How about 
Malfoy and Potter?" said Snape with a twisted smile.

   <various stuff with Lockhart>

   Snape moved closer to Malfoy, bent down and whispered something in 
his ear.  Malfoy smirked too. . . .

   Malfoy raised his wand quickly and bellowed "Serpensortia!"
   The end of his wand exploded.  Harry watched, aghast, as a long 
black snake shot out of it, fell heavily onto the floor between them 
and raised itself, ready to strike. . . .
   "Don't move, Potter," said Snape lazily, clearly enjoying the sight 
of Harry standing motionless, eye to eye with the angry snake.  "I'll 
get rid of it. . ."

   <Lockhart scares it towards Justin, Harry makes it stop, Justin 
reacts angrily>

   Snape stepped forward, waved his wand and the snake vanished in a 
small puff of black smoke.  Snape, too, was looking at Harry in an 
unexpected way:  it was a shrewd and calculating look, and Harry 
didn't like it.

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So, to my question:  of all the things he could do, why does Snape 
cause Draco to set a snake on Harry?

Does Snape already suspect Harry of knowing Parseltongue?  What would 
give him that idea before this incident?

Does he suspect him of being the Heir of Slytherin even before this 
incident?  Again, why would he?

Or did he just suggest a nasty spell and didn't have any idea that a 
snake would reveal something telling about Harry?  His "shrewd and 
calculating" look could just mean he's wondering =now=, or that he now 
sees a way to give Potter a very hard time.

Amy Z

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 However, it is easy to repulse the Pogrebin 
 with simple hexes or Stupefying Charms.  
 Kicking has also been found effective.
     -Fantastic Beasts and Where to Find Them
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